Abstract. A lattice model of $d$-dimensional quantum anharmonic oscillators with a
polynomial anharmonicity and a ferroelectric interaction is considered. For
arbitrary $d\in {I\!\! N}$, it is shown that the critical fluctuations of the
position operator, peculiar to the critical point, are suppressed at all
temperatures provided the particles are "strongly quantum". The latter means
that for the corresponding one-dimensional model, the smallest distance between
the energy levels of the isolated oscillator is large enough or that the reduced
mass of the oscillator is less than some threshold value depending on the
anharmonicity parameters. These results are the extension to the vector case of
the statements obtained recently in \cite{[00]} and \cite{[0]} regarding such
effects in similar lattice models.